谐振子薛定谔方程的简单解法

物质的许多物理与化学性质都可以用线性谐振子模型解释，本文用简单的数学运算求解线性谐振子的薛定谔方程，避免了特殊函数等复杂的数学运算，得出了量子力学教材完全相同的结果。     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

高阶半线性抛物型方程组的生命跨度

其中m,P,q>1．利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计．     

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

加权Herz—type Triebel—Lizorkin空间的特征及应用

当s∈ R,0,〈q, p〈∈∞,0,〈β≤∞且 max{-n/q,-nδ2/qδ1}〈a时，定义了加权Herz—type　Triebel-Lizorkin空间kq^q,pF^s β（R^n,ω1，ω2）和Kq^a,pF^sβ（R^n，ω1，ω2），并给出这些空间的一些特征及在这些空间上的Hard—Littlewood极大算子不等式．     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Thermodynamic derivative properties and densities for hyperbaric gas condensates: SRK equation of state predictions versus Monte Carlo data

The ability of Soave–Redlich–Kwong cubic equation of state (SRK EoS) to predict densities and thermodynamic derivative properties such as thermal expansivity, isothermal compressibility, calorific capacity, and Joule–Thompson coefficients, for two gas condensates over a wide range of pressures (up to 110 MPa) was studied. The predictions of the EoS were compared to Monte Carlo simulation data obtained by Lagache et al. [M.H. Lagache, P. Ungerer, A. Boutin, Fluid Phase Equilibr. 220 (2004) 221]. Two completely different alpha functions for the SRK EoS attractive term were used and their respective effects on the predictions of such properties were analyzed. Also, two different forms of the crossed terms of the attractive parameter, a_ij, and three expressions of the crossed terms of the repulsive parameter, b_ij, were combined in different ways, and predictions were carried out. Little sensitivity of the properties on the chosen alpha function, except for the calorific capacities, was found in the systems studied. The most commonly used combination rules to model phase behavior of reservoir fluids, i.e. geometric and arithmetic forms of a_ij and b_ij, respectively, predicted very deficient results for these fluids at extreme conditions, specially for density calculations.     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.